Ten thieves

Here is a nice short easy puzzle.

Puzzle

Ten thieves have just made off with 56 identical rare gemstones. They realize that it is impossible for each thief to receive an equal number of the gems, but as it turns out, there are just enough senior thieves so that each of them can get exactly one more of the gems than each of the junior thieves. How many senior thieves were there, and how many gems did each thief get?

Help

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Hint

What is 56 divided by 10?

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Answer

There are 6 senior thieves, who each received 6 gems, while the 4 junior thieves received only 5

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Solution

While there are algebraic ways to solve the puzzle, the easiest method is to realize that each of the ten thieves must receive at least 5 gems (since 5 times 10 is 50. This leaves 6 gems left over. We know that there were just enough senior thieves for them to each receive an extra gem, so there must be exactly 6 senior thieves.

References

The Riddle of Scheherazade: And Other Amazing Puzzles by Raymond Smullyan.